Computational Dynamics (PDF)

Preface. 1 Introduction. 1.1 Computational Dynamics. 1.2 Motion and Constraints. 1.3 Degrees of Freedom. 1.4 Kinematic Analysis. 1.5 Force Analysis. 1.6 Dynamic Equations and Their Different Forms. 1.7 Forward and Inverse Dynamics. 1.8 Planar and Spatial Dynamics. 1.9 Computer and Numerical Methods. 1.10 Organization, Scope, and Notations of the Book. 2 Linear Algebra. 2.1 Matrices. 2.2 Matrix Operations. 2.3 Vectors. 2.4 Three-Dimensional Vectors. 2.5 Solution of Algebraic Equations. 2.6 Triangular Factorization. 2.7 QR Decomposition. 2.8 Singular Value Decomposition. Problems. 3 Kinematics. 3.1 Kinematics of Rigid Bodies. 3.2 Velocity Equations. 3.3 Acceleration Equations. 3.4 Kinematics of a Point Moving on a Rigid Body. 3.5 Constrained Kinematics. 3.6 Classical Kinematic Approach. 3.7 Computational Kinematic Approach. 3.8 Formulation of the Driving Constraints. 3.9 Formulation of the Joint Constraints. 3.10 Computational Methods in Kinematics. 3.11 Computer Implementation. 3.12 Kinematic Modeling and Analysis. 3.13 Concluding Remarks. Problems. 4 Forms of the Dynamic Equations. 4.1 D'Alembert's Principle. 4.2 D'Alembert's Principle and Newton-Euler Equations. 4.3 Constrained Dynamics. 4.4 Augmented Formulation. 4.5 Lagrange Multipliers. 4.6 Elimination of the Dependent Accelerations. 4.7 Embedding Technique. 4.8 Amalgamated Formulation. 4.9 Open-Chain Systems. 4.10 Closed-Chain Systems. 4.11 Concluding Remarks. Problems. 5 Virtual Work and Lagrangian Dynamics. 5.1 Virtual Displacements. 5.2 Kinematic Constraints and Coordinate Partitioning. 5.3 Virtual Work. 5.4 Examples of Force Elements. 5.5 Workless Constraints. 5.6 Principle of Virtual Work in Statics. 5.7 Principle of Virtual Work in Dynamics. 5.8 Lagrange's Equation. 5.9 Gibbs-Appel Equation. 5.10 Hamiltonian Formulation. 5.11 Relationship between Virtual Work and Gaussian Elimination. Problems. 6 Constrained Dynamics. 6.1 Generalized Inertia. 6.2 Mass Matrix and Centrifugal Forces. 6.3 Equations of

Ahmed Shabana, University of Illinois, USA, is the Richard & Loan Hill Professor of Engineering in the Department of Mechanical Engineering at the University of Illinois at Chicago. He is the author of a number of books, including Dynamics of Multibody Systems, Vibration of Discrete and Continuous Systems, and Theory of Vibration: An Introduction.

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